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Yakvenalex [24]
3 years ago
6

Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (1,-7) and has (2,- 4) as its vertex. What i

s the standard form of the equation?
Mathematics
1 answer:
Anettt [7]3 years ago
5 0
The coordinates of the vertex are (h,k)  so we can write:-
 f(x) = a(x -2)^2 - 4
now when f(x) = -7 x = 1 so:-

-7 = a(1-2)^2 - 4
-7 = a - 4
a = -3

so the vertex formula is 
f(x) = -3(x - 2)^2 - 4

standard form:-

f(x) = -3(x^2 - 4x + 4)  - 4
       = -3x^2 + 12x - 16
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Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10
Vladimir [108]

Answer:

0011100000

1010010001

0111001110

Step-by-step explanation:

As the question is not complete, Here is the complete question.

Suppose that the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Express each of these sets with bit strings where the ith bit in the string is 1 if i is in the set and 0 otherwise.

a) {3, 4, 5}

b) {1, 3, 6, 10}

c) {2, 3, 4, 7, 8, 9}.

So, we need to express a) b) and c) into bit strings.

Firstly, number of elements in the universal set represent the number of bits in the bit string.

Secondly, 1 = yes element is present in both universal set as well as in sub set.

0 = No, element is not present in sub set but present in universal set.

Hence, we have:

a) Sub set {3,4,5} = 0011100000  (As there are 3 1's which means only 3,4,5 are present in both universal set and subset.

Similarly,

b) Sub set {1, 3, 6, 10} = 1010010001

c) Sub set {2, 3, 4, 7, 8, 9} = 0111001110

5 0
3 years ago
Savannah is planning to buy enough raffle
Alborosie

Answer:

20 tickets

Step-by-step explanation:

tickets/total tickets * 100% = 10% chance to win the raffle

x/200*100=10

solve for x

x/200 =  10/100

x = 200(0.1)

x = 20

6 0
3 years ago
$10,000 for 5 years at 4% interest
inessss [21]

Simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.

As given in the question,

Simple Interest:

The simple interest is an amount that is paid for loan or borrowed money over a certain period at a fixed percentage of borrowed money.

Principal amount:

Principal amount is the money that is taken as loan or borrowed.

Formula of Simple Interest:

Simple interest = Principal amount × Rate × Time

Since,

Principal amount = $10,000

Rate = 4% per year

Time = 5 years

Then,

Simple interest = 10,000 × 4 × 5

Simple interest = $ 12000

Total value after 5 years = $ 12000

Principal amount = $ 10000

Interest Earned = (Total value) - (Principal amount)

Interest Earned = $ 12000 - $ 10000

Interest Earned = $ 2000

Therefore, simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.

The complete question is:

Fabian is taking out a loan in the amount of $10,000. His choices for the loan are a 5-year loan at 4% rate of interest .What is the amount of simple interest and interest earned Fabian would have to pay?

To know more about simple interest here

brainly.com/question/25845758

#SPJ1

3 0
10 months ago
A lawn sprinkler spins in a circle. The sprinkler covers a radius of 12 feet. Which choice is the closest to the area of lawn th
Veronika [31]

You would do pi x r squared. r=12, and 12 squared is 144. pi (3.14) times 144 equals 452.16!

3 0
3 years ago
Arrange the events in Polish history in chronological order using the numbers 1-6.
Basile [38]

Answer:

3

5

1

2

4

6

Yan po para sa akin.

4 0
2 years ago
Read 2 more answers
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